grpp_specfunc_scaled_mod_sph_bessel.c File Reference

#include <math.h>
#include "grpp_specfunc.h"
#include "libgrpp.h"

Go to the source code of this file.

Macros
#define	M_PI   3.1415926535897932384626433
#define	LMAX   (LIBGRPP_MAX_BASIS_L + LIBGRPP_MAX_RPP_L)
#define	NPOINTS   2000

Functions
static double	modified_scaled_bessel_derivative (int n, int lambda, int ix)
static double	bessel_asymptotic_R_function (int n, double x)
void	libgrpp_pretabulate_bessel ()
double	libgrpp_modified_bessel_scaled (int n, double x)

Variables
double	bessel_table [NPOINTS][3 *LMAX][10]
const double	rfun_coeffs [50][50]
const double	bessel_table_0 [1601][60]

Macro Definition Documentation

M_PI

#define M_PI   3.1415926535897932384626433

Definition at line 17 of file grpp_specfunc_scaled_mod_sph_bessel.c.

LMAX

#define LMAX   (LIBGRPP_MAX_BASIS_L + LIBGRPP_MAX_RPP_L)

Definition at line 26 of file grpp_specfunc_scaled_mod_sph_bessel.c.

NPOINTS

#define NPOINTS   2000

Definition at line 31 of file grpp_specfunc_scaled_mod_sph_bessel.c.

Function Documentation

modified_scaled_bessel_derivative()

static double modified_scaled_bessel_derivative ( int  n, int  lambda, int  ix  )

static

Calculates n-th order derivative on the scaled modified spherical Bessel function K_lambda(z).

Note that the formula (45) for derivatives in the paper of Flores-Moreno et al is wrong (you must also add: - K^(n-1)_{lambda}).

R. Flores-Moreno, R. J. Alvarez-Mendez, A. Vela, A. M. Koster, Half-numerical evaluation of pseudopotential integrals. J. Comput. Chem. 27 (9), 1009 (2006), doi: 10.1002/jcc.20410

Definition at line 132 of file grpp_specfunc_scaled_mod_sph_bessel.c.

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bessel_asymptotic_R_function()

static double bessel_asymptotic_R_function ( int  n, double  x  )

static

Asymptotic formula for the scaled spherical modified Bessel function of order 'n'.

For the formula, see: R. Flores-Moreno, R. J. Alvarez-Mendez, A. Vela, A. M. Koster, Half-numerical evaluation of pseudopotential integrals. J. Comput. Chem. 27 (9), 1009 (2006), doi: 10.1002/jcc.20410

In the optimized version all factors used are pretabulated above in the 'rfun_coeffs' array. Unoptimized version of this code:

double sum = 0.0;

for (int k = 0; k <= n; k++) { sum += factorial(k + n) / (factorial(k) * factorial(n - k) * pow(2 * x, k)); }

Definition at line 175 of file grpp_specfunc_scaled_mod_sph_bessel.c.

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libgrpp_pretabulate_bessel()

void libgrpp_pretabulate_bessel

(

)

Definition at line 48 of file grpp_specfunc_scaled_mod_sph_bessel.c.

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libgrpp_modified_bessel_scaled()

double libgrpp_modified_bessel_scaled	(	int	n,
		double	x
	)

Definition at line 68 of file grpp_specfunc_scaled_mod_sph_bessel.c.

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Variable Documentation

bessel_table

double bessel_table[NPOINTS][3 *LMAX][10]

Definition at line 39 of file grpp_specfunc_scaled_mod_sph_bessel.c.

rfun_coeffs

const double rfun_coeffs

Definition at line 194 of file grpp_specfunc_scaled_mod_sph_bessel.c.

bessel_table_0

const double bessel_table_0[1601][60]

extern

Definition at line 34 of file grpp_specfunc_bessel_table.c.